Financial Engineering and Actuarial Science In the Life Insurance - PowerPoint PPT Presentation

Financial Engineering and Actuarial Science In the Life Insurance Industry Presentation at University of California at Santa Barbara February 21, 2014 Frank Zhang, CFA, FRM, FSA, MSCF, PRM Vice President, Risk Management Pacific Life Insurance Company

Disclaimer This presentation contains the current opinions of the author and not of my employer Pacific Life Insurance Company or the Society of Actuaries. Any such opinions are subject to change without notice. This presentation is distributed for educational purposes only. 2 2

Table of contents  Traditional insurance and risk management  Variable annuities as a newer generation of hybrid products  Financial engineering and actuarial science as a new practice for variable annuities 3 3

Traditional insurance based on averages  Traditional insurance products with mortality, longevity, morbidity, etc. may be diversified  Most products can be safely priced based on actuarial expected values (averages) and standard deviation  Typical actuarial risk management techniques ⇒ Test sensitivities of assumptions ⇒ Test of distributions and tails 4 4

A flaw of traditional averages – extreme cases 5 5

Law of large numbers  To reduce the uncertainty (risk or standard deviation) of the expected outcome ⇒ Sell a large number of small amount of insurance  The old and true statistical principle of “law of large numbers” ⇒ Statistically speaking, larger samples reduce “sample error” 6 6

Worked well with tail risk management, until …  Risk mitigations ⇒ Cut off the tails with caps in insurance coverage (to make sure no single case is too large to kill like the crossing river example) ⇒ Sell more to diversify ⇒ Be prepared for rare but extreme pandemic events (systemic)  Actuarial risk analysis ⇒ Stochastic simulations and principle-based valuation ⇒ Look at more than the averages but also the distributions ⇒ Look at percentiles and use CTEs for tail risk  Worked well with traditional life and annuity products, until recently ⇒ Core insurance expertise is to pool diversifiable risks ⇒ How about newer generation of products, such as variable annuities? 7 7

Table of contents  Traditional insurance and risk management  Variable annuities as a newer generation of hybrid products  Financial engineering and actuarial science as a new practice for variable annuities 8 8

Variable annuity (VA)  Life insurance products are increasingly derivatives oriented and many of the same derivatives valuation techniques apply  The hybrid products also create unique challenges and opportunities to actuaries and financial engineers  Variable annuity is a retirement investment account sold by life insurers ⇒ Underlying investments are generally “mutual funds” of various asset classes ⇒ Contract holders pay insurer and mutual fund manager fees over time ⇒ The account value can go higher or lower due to investment results ⇒ Guarantee payoffs = f( guaranteed amount - total basket value of mutual funds) ⇒ Death benefit is paid when a) The account value is lower than principal and b) Policyholder died ⇒ Living benefits can be paid without having to die, based on different designs such as accumulation guarantees (wait for 10 years), withdrawal benefits (guaranteed withdrawal amounts, regardless of investment performance), etc. ⇒ Policyholders keep upside potential of the account performance – and insurance company provides the downside guarantees (put options!) ⇒ Many VA contracts have much more exotic benefits ⇒ Traditionally, policyholder may or may not exercise optimally 9 9

Life insurance or derivatives? Variable annuity (VA) guarantees blur the boundary between derivatives products and traditional life insurance products: Living or dying! Life Variable Derivatives Insurance Annuities Diversifiable Non-diversifiable Law of large numbers Derivatives pricing Dynamic Mutual Policyholder Funds Behavior Multiple underlying assets Path Dependence VA contracts invest in mutual funds, paying fees to insurer, and getting guarantee benefits GMDB (Guaranteed Minimum Death Benefit) => Payable at death VAGLB (Variable Annuity Guaranteed Living Benefit) => Payable Under Predefined Conditions: GMAB (Guaranteed Minimum Accumulation Benefit) for account value guarantee GMIB (Guaranteed Minimum Income Benefit) for annuitized payouts guarantee GMWB (Guaranteed Minimum Withdrawal Benefit) for withdrawals guarantee 10

Sample VA GMDB designs  Different strikes for different designs Return of premium : strike = initial AV = initial premium deposits Ratchet : discrete look back strike = max (sample AVs during the contract life) Rollup : increasing strikes at an annual rate x: strike t = (1+x) t Combinations : strike = max of ratchet and rollup 11

GMDB pricing Benefit paid upon death Death benefit paid upon death Rate of mortality based on law of large numbers Mortality rates increase quickly at older ages 12

GMDB pricing Benefit paid only If GMDB contract stays in force at death Not all contracts initially issued still in force in later years People could lapse the contract or annuitize (decrements) 13

How to price VA embedded derivatives Risk neutral valuation using stochastic simulations GMDB is paid only If GMDB is in the money and still In force at death Price = sum of all future possible death payoffs on surviving contracts (by simulations) 14

Table of contents  Traditional insurance and risk management  Variable annuities as a newer generation of hybrid products  Financial engineering and actuarial science as a new practice for variable annuities 15 15

Capital market risk management  Capital markets represented by Wall Street and portfolio investments  Traditional investments in fixed income (bonds), equity (stocks), and modern derivatives (options) ⇒ Fixed income portfolio management focuses on interest rate risk and credit risk ⇒ Equity investment focuses on systematic risk (measured by beta) ⇒ Derivatives are priced using financial engineering techniques  Financial engineering is based on “law of one number” or no arbitrage  Wall Street has used financial engineering to price and manage the risks for derivatives 16 16

Annuity derivatives vs. mortgage backed securities 17 17

Annuity derivatives pricing challenges Comparison - Variable annuities • Variable annuities are sold to individual investors who pay money to insurance company. • VAs pass through mutual fund performance BUT add derivatives guarantees • There is no active secondary market who collect the investments from the investor 18

Annuity derivatives pricing challenges Comparison - Mortgage backed securities • Mortgages are sold to banks/institutional investors who pay money to fund houses. • The funding needs created secondary MBS markets • MBS are created to pool mortgages. 19

Annuity derivatives pricing challenges Dynamic policyholder behavior modeling  Dynamic policyholder behavior modeling is critical & difficult ⇒ Key driver for pricing but options not always exercised optimally ⇒ Mortality risk managed by pool of large numbers but living benefits much more challenging ⇒ Behavior very difficult to predict and with little or no experience ⇒ Policyholder dynamics causing significant gamma exposure ⇒ Capital market risks not diversifiable as insurance risks  MBS prepayment vs. annuities dynamic policyholder behavior modeling ⇒ MBS prepayments based on real world experience or expectations but validated by active capital market MBS prices, unlike annuities ⇒ Risk neutral pricing standard in financial engineering, but transition from actuarial expectations to risk neutral pricing caused confusions about probability distributions and stochastic simulations ⇒ MBS markets not usually concerned with nested stochastic projections that mix risk neutral world and risk neutral valuations, unlike annuities 20 20

Insurance or mortgage cash flows vs. derivatives averaging Be careful when using cells to average the derivatives 21

Derivatives, VA and fixed indexed annuities  Options are capital market instruments  Puts and calls have non-linear payoffs ⇒ Only when stock price ends below or higher than the put/call strike respectively ⇒ The options are highly leveraged with small option premium for potentially large payoffs  VA writers sold short put options in GMDB and VAGLB as embedded benefits  Fixed indexed annuity (FIA) writers sold short of call/call spread options Potentially large payoff Small premium 22

Some things cannot be averaged Source: Simon Proctor 23 23

Derivatives cannot be averaged  Selling 10% in-the-money put and 10% out-of-money put is not the same as selling an at-the-money put  Shorting call and put at the same strike might offset the directional stock movements but still leaves exposure to market volatility 24

Capital market law of one number (price)  Financial engineering is based on “law of one number” or no arbitrage  No arbitrage means no risk-free way of making money and there is only one price that is the market price 25 25